The Arnold Group at Princeton University
Viscoelastic jet formation with impulsive boundary motion using Basilisk
Emre Turkoz, Luc Deike, Craig B. Arnoldwith Jens Eggers
November 16th, 2017Princeton,NJ
J. Fluid Mech. (2012), vol. 709, pp. 341–370
Motivation
Need of Printing Viscoelastic MaterialsFlexible electronics Sensors
Tissue engineering3D printing
Dababneh, J. Manuf. Sci. Eng 136(6), 061016 (2014) Muth, Adv. Mater. 26, 6307-6312 (2014)
Azimi, Environ. Sci. Technol 50, 1260-1268 (2016) Koch, Biotech. Bioeng. 109.7 (2012)
Motivation
Printing TechniquesInkjet printing Laser-induced forward
transfer
● Nozzle should be designed for the ink and application
● Clogging● Drop diameters ≥ 10 μm
● No nozzle → no clogging● Droplets with smaller
diameters
Description of our technique
Blister-Actuated Laser-Induced Forward Transfer (BA-LIFT)
J. Fluid Mech. (2012), vol. 709, pp. 341–370Microfluid. Nanofluid. 11.2, 199-207 (2011)
Droplet pinch-off through Rayleigh-Plateau instability
Material transfer onto acceptor surface
Mechanical impulse and subsequent jet formation
Parameter Space BA-LIFT has many parameters
5
NMP - A newtonian solvent
0.1 wt.% xanthan gum in water - A viscoelastic solution
Eb: Laser beam energy
Rb: Laser spot sizeHp: PI layer thickness
H: Film thicknessμ: Viscosity⍴: Density
�: Surface tensionλ: Viscoelasticity
Blister profile Ink properties
Jet formation
This parameter space determines the outcome of the process
Problem StatementOutline of our study
6
Develop a fully adaptive Basilisk model to simulate BA-LIFT with Newtonian fluids
Determine the dimensionless
parameters
Solid boundary deformation
Grid convergence with static and
adaptive meshing
Validation with experiments
Validate the viscoelastic models in Basilisk with the literature
Modify the BA-LIFT model slightly by introducing an extra dimensionless
parameter
Transfermodel
Problem SetupHow the computation domain should look like
7[1] J. Fluid Mech. (2012), vol. 709, pp. 341–370
Flow is axially symmetric
Solid boundary deformation: From empirical measurements [1]
Air
Three phases- Polymer- Ink- Air
Empirical formula for blister expansion
8
Impulsive Boundary Deformation- Boundary deformation during BA-LIFT is already
formulated [1]
[1] Brown, M. S., Brasz, C. F., Ventikos, Y., & Arnold, C. B. (2012). Impulsively actuated jets from thin liquid films for high-resolution printing applications. Journal of Fluid Mechanics, 709, 341-370.
Empirical profile fits for blister profiles
Dimensionless parameters
9
Non-dimensionalization of the Problem
μa Air viscosity
μl Liquid viscosity
⍴a Air density
⍴l Liquid density
� Surface tension
�b Blister expansion time
Rb Blister radius
Experimental parameters
Dimensionless numbers
Blister expansion time / capillary time scale
Modeling the solid layer [1,2,3] & Algorithm
Implementation of the solid layer
- Solid layer is represented with a tracer (f12) - Reinitialized every time step- Velocity values throughout the solid are assigned at each
time step
[1] Lin-Lin, Z., Hui, G., & Chui-Jie, W. (2016). Three-dimensional numerical simulation of a bird model in unsteady flight. Computational Mechanics, 58(1), 1-11.[2] Wu, C. J., & Wang, L. (2007). Direct numerical simulation of self-propelled swimming of 3d bionic fish school. Computational Mechanics, Proceedings of ISCM.[3] http://basilisk.fr/sandbox/popinet/movingcylinder.c
10
Advance the solid boundary
Reinitialize the velocity everywhere
in the solid
Calculate material properties
Symmetry axis
Every timestep!
Adaptive grid for parallelization
11
Results
Grid Convergence
Comparison of different parallelization schemes
12
7 8 9 10 11
1.34 2.67 5.34 10.68 21.37
Level
cells/μm
Validation with Experiments
Comparison with experiments
13
Now: Viscoelastic ModelsSimulations for Newtonian BA-LIFT are completed
14
Develop a fully adaptive Basilisk model to simulate BA-LIFT with Newtonian fluids
Determine the dimensionless
parameters
Solid boundary deformation
Grid convergence with static and
adaptive meshing
Validation with experiments
Verify the viscoelastic models in Basilisk with the literature
Modify the BA-LIFT model by introducing an extra dimensionless parameter to model
viscoelasticity
Transfermodel
A Sidetrack from BA-LIFT: Viscoelastic Simulations in Basilisk
The log-conformation technique
15
- Possible thanks to the model [1] implemented by Jose M. Lopez-Herrera Sanchez [2]- Log-conformation technique to overcome “the high-Weissenberg
number problem”
[1] R. Fattal and R. Kupferman. Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. Journal of Non-Newtonian Fluid Mechanics. 1, pp. 23–27, (2005).[2] http://basilisk.fr/sandbox/lopez/log_conform_1.h
Oldroyd-B
FENE-P
Conformation tensor!
Verifying the Oldroyd-B model: Comparison with Clasen [1]
Comparison with a 1D explicit finite-difference solution of Oldroyd-B model
16[1] Clasen, C., Eggers, J., Fontelos, M. A., Li, J., & McKinley, G. H. (2006). The beads-on-string structure of viscoelastic threads. Journal of Fluid Mechanics, 556, 283-308.
Symmetry axis
2D axially symmetricLog-conformation
technique1D along the axial
directionFinite-difference
Slender jet equations
Clasen [1] Basilisk
Symmetry BC
Experimental image sequence
Minimum Filament Radius vs. Time
Filament thinning
17
Oldroyd-B with Basilisk: Accuracy
The model can not capture the experimental trends
18
Oldroyd-B with Basilisk: Accuracy
The model can not capture the experimental trends
19
Slope for the axial stress should be
improved!
A different strategy to solve Oldroyd-B
equations?
A note on Oldroyd-B: Comparison with Experiments
The model can not capture the experimental trends
20
Experimental thinning is faster
at early times
[1] Clasen, C., Eggers, J., Fontelos, M. A., Li, J., & McKinley, G. H. (2006). The beads-on-string structure of viscoelastic threads. Journal of Fluid Mechanics, 556, 283-308.
Simulating BA-LIFT with Oldroyd-B and FENE-PThe last step: BA-LIFT simulations with the current models
21
Develop a fully adaptive Basilisk model to simulate BA-LIFT with Newtonian fluids
Determine the dimensionless
parameters
Solid boundary deformation
Grid convergence with static and
adaptive meshing
Validation with experiments
Verify the viscoelastic models in Basilisk with the literature
Modify the BA-LIFT model by introducing an extra dimensionless parameter to model
viscoelasticity
Transfermodel
Unique Jet Features during BA-LIFT with Viscoelastic Inks
Viscoelastic BA-LIFT simulations
22Shoulder formation
Hanging drop formation and delayed breakup
Jetting without breakup
Multiple-drop formation
42 us22 us 62 us >1s342 us292 us
Droplet shape!
Viscoelastic BA-LIFT simulations
0.1 wt.% PEO in 60-40 wt.% WG
Strategy: Try to observe these features with a parameter sweep and compare with experimental
parameters!
Viscoelastic BA-LIFT simulations
24
De = 160Oldroyd-B model
Oldroyd-B model
Infinitely stretchable
polymer chains
Can resolve with uniform
mesh level 11
Could not get adaptive meshing +
MPI work with viscoelastic model
yet!
Future Work
Maybe the answer lies in a new model!
25[1] Eggers, J. (2014). Instability of a polymeric thread. Physics of Fluids, 26(3), 033106.
Later stages: Beads-on-a-
string formation
A model proposed in [1] to explain this
sinusoidal instability!
Implement refinement
with filament radius
Make it work with adaptive
and MPI
Acknowledgements
The end
26
- Members of the Arnold group
- Jose M. Lopez-Herrera Sanchez for numerous e-mail exchanges
- Prof. Jens Eggers
- Antonio Perazzo and Prof. Howard A. Stone
Future Work: We need to implement a better model! [1]
Maybe the answer lies in a new model!
27[1] Eggers, J. (2014). Instability of a polymeric thread. Physics of Fluids, 26(3), 033106.
Perturbation analysis yields a novel mechanism for an instability which
grows sinusoidally and might explain the formation of beads-on-a-string structure
Experimental observation: Polymer concentration is very high along the
thread
n Polymer number density
�p Polymer stress component
�s Solvent viscosity
� Relaxation time
D Diffusivity of polymer in the solvent
� Unit tensor
Algorithm for Log-conformation Technique (as in log_conform_1.h by Lopez)
The end
28
Initialize parametersS, (tensor
type)
Assign Neumann BC
for S and except for the
axi bottom
Evaluate A from S
Diagonalize A and evaluate
Evaluate B, M and
1Evaluate the RHS of (2)
Calculate (1)
Integrate (2)2
Recover the conformation
tensor
3Integrate (3)
analytically
Evaluate the stress tensor S
for the next time step
Minimum Filament Radius vs. Time
Filament thinning
29
De De*
94.9 0.2520 96.57
60 0.3045 56.84
50 0.3343 48.34
40 0.3835 38.46
De De*
94.9 0.2520 96.57
60 0.3045 56.84
50 0.3343 48.34
40 0.3835 38.46
Effect of elasticity on BA-LIFT jetsStill localized pinch-off & beads-on-a-string not
observed
Viscoelastic BA-LIFT simulations
30
De = 0.2Oh = 0.2b=1000
De = 0.4Oh = 0.2b=1000
De = 0.6Oh = 0.2b=1000
Maximum Axial Stress along the Filament vs. Time
Filament thinning
31
De De*
94.9 0.2374 7.564 77.88
60 0.3045 5.063 47
50 0.3343 4.616 43.75
40 0.3835 3.918 35.43
De De*
94.9 0.2374 7.564 77.88
60 0.3045 5.063 47
50 0.3343 4.616 43.75
40 0.3835 3.918 35.43